In many research and development (R&D) experiments, an experimental trial run is carried out by a researcher who first makes changes to a process, elements of a process, or study factors of the experiment (i.e., system level). After making these changes, the researcher then obtains measurements on test samples obtained from the trial which are referred to herein as experiment results. From these experimental results, the researcher seeks typically to identify and quantify the impacts and effects of the changes that were made.
The data structure common to these types of experiments is a single resulting measurement on a single sample obtained from the trial by the researcher. This resultant may then be represented as a response value in a coordinated manner, such as in a graph for instance. Graphically, the resultant would have a single response value (i.e., “Y-axis” data value) associated with the study factor level settings (i.e., “X-axis” data values). By example and not by way of limitation, a Y-axis data value may have an associated measurement time while an X-axis data value may represent the operational setting of a processes parameter. This type of data structure enables researchers and others the ability to identify and quantify the effects of the changes to the study factors of the experiment by numerical analysis methodologies.
However, when experimental error is a concern, which is often the situation, it is desirable to test more samples to lessen influences of error. For instance, the Y-axis data are often expanded by testing more samples from the trial and/or conducting more repeat tests per trial sample. In such situations, it is typically the standard practice to “reduce” the trial Y-axis data for numerical analysis purposes to the simple form of a single Y-axis data value associated with the trial X-axis data. This reduction is routinely done by calculating the arithmetic average of the trial Y-axis data and associating the single average, or the mean value, of the Y-axis data with the X-axis data. Depending on the experiment, additional other standard reductions of Y-axis data, such as the variance or the standard deviation for instance, may be computed to provide additional information as to variations of the system in response to the study factor level settings.
However, certain types of R&D, experiments, such as those in synthetic chemistry development or drug product dosage form development (e.g. tablet or gel cap) for instance, may have trial runs where each trial run has an associated response data set consisting of multiple, intrinsically-related values.
For example, in a drug tablet development experiment, a typical critical response is the rate of drug release over time as the tablet dissolves, often referred to as the “drug release profile”. Measuring the unit amount of the drug released into a solution every ten (10) minutes for twelve (12) hours as the tablet dissolves, for example, will yield seventy-two (72) time-related response values (i.e., Y-axis data values) for the trial. In this situation, the multiple Y-axis data columns representing time-based measures of a response (i.e., the 12 hour drug release profile) would need to be reduced to one or more single Y-axis data values that characterize and quantify the profile to identify and quantify the effects of the study factor changes on the critical characteristics of the profile by numerical analysis methods.
However, standard response reductions of time-related Y-axis data values associated with a trial, such as the mean value, variance, and standard deviation, do not represent the drug release profile in a meaningful way to researchers. Additionally, it is clear that more than one repeat measurement may be made at each time point or interval. Therefore, in this case for instance, the response profile data set has two levels of complexity: multiple time-related measurement points consisting of multiple test measurements at each point in time.
By further example, in drug product dosage form development experiments, often an objective of the activity is identifying the study factor settings that may result in a specific target release profile. Currently, to identify and quantify the effects of study factor changes by numerical analysis methods a researcher must manually carry out a number of complex data handling, conversion, and reduction operations to generate results, profile data and then to derive scalar response data sets appropriate to numerical analysis from the profile data.
FIG. 1 depicts a graph 100 of drug release profile data from six experiment trials conducted as part of a drug tablet development experiment. In each trial the original response data value obtained at each X-axis time point was the Amount of the drug measured in the time point sample. The graphed % Dissolved response data value associated with each time point in each time in each trial profile therefore represents a conversion of the original Amount data value into a % Dissolved data value; the conversion being necessary to construct a response profile for the trial. When more than one measurement is carried out on each time point sample obtained from a trial, the arithmetic average, or mean, of the repeat Amount measurements must first be obtained prior to conversion of the mean value into a % Dissolved data value. Thus, in this case two conversions of the original Amount data from a trial would be required in order to obtain the % Dissolved profile for the trial. Once the profile is constructed, further conversions or reductions must be carried out on the profile data to obtain one or more scalar response data sets appropriate to numerical analysis.
From the response profile data sets graphically depicted in FIG. 1, one of the responses that can be determined and depicted is percent of tablet dissolved (Y-axis data along the ordinate) versus time interval (X-axis data along the abscissa).
From FIG. 1, a particular response of interest is the percent of drug dissolved at the 120 minute time point, shown along line 110. The researcher's compilation compiled of this scalar response (single Y column) was performed with a great deal of effort by selecting the percent release (i.e., dissolved) value at 120 minutes from each trial runs' profile data set. This effort represents the simplest reduction of a response profile data set to a scalar response.
From FIG. 1, a further particular response of interest may be the drug release rate in a specific time interval such as between two and eight hours (i.e., the 120-480 minute segment of the graphed profiles) which is depicted by boxed area 120. To determine a related scalar response, a more complex reduction of the release profile data is required and is even more challenging for a researcher to undertake.
One method of attempting to resolve this issue is for the researcher to extract the 120-480 minute portion of the percent released data from each profile and then calculate the slope of the extracted data (i.e., the change in percent released divided by change in time). Researchers are often challenged in determining scalar response data sets such as this from time-related profile data sets.
In many situations, the target response profile is linear, but in many cases a non-linear (i.e., curved) profile is often desired. To obtain reductions of curved profile data, the curved target profile must first be defined.
One typical step in defining the curved target profile is to individually define the X-Y coordinate data (i.e., coordinates) corresponding to the desired curve along the X-axis interval of interest. To correctly estimate the degree of similarity of an experimentally obtained response profile to a target profile using numerical analysis techniques typically necessitates that both data sets have the same number of data values with the same X-axis coordinates. A researcher's construction of such a target profile data set is indeed quite challenging, tedious and error-prone, particularly given the large number of individual X-Y data pair values that must be defined. For example, seventy-two (72) X and Y values in the 12-hour release profile data are required as previously set forth.
In some cases though a general equation may exist that generally approximates the target profile. In such a situation, the researcher can input the X value at each measurement time point into the equation and obtain the corresponding Y value as the equation output. While this generalization may simplify the researcher's task of constructing the target profile data set, the equation must often be adjusted when its output profile differs from the target profile. This adjustment can be a challenge to the researcher as well, particularly given the need for advanced numerical analysis and equation-building skills which are typically beyond the capabilities of many practicing researchers.
Therefore, it can be and is readily determined that a visually and graphically oriented method and system for enabling the generation of reduced response data sets from complex experimental results is desired. Additionally, it is preferred that such a method and system would also properly format the data sets for numerical analysis for the researchers' use and benefit.